• Title/Summary/Keyword: wave equation

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SH-wave in a piezomagnetic layer overlying an initially stressed orthotropic half-space

  • Kakar, Rajneesh;Kakar, Shikha
    • Smart Structures and Systems
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    • v.17 no.2
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    • pp.327-345
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    • 2016
  • The existence of SH-wave in a piezomagnetic layer overlying an initially stressed orthotropic half-space is investigated. The coupled of differential equations are solved for piezomagnetic layer overlying an orthotropic elastic half-space. The general dispersion equation has been derived for both magnetically open circuit and magnetically closed circuits under the four types of boundary conditions. In the absence of the piezomagnetic properties, initial stress and orthotropic properties of the medium, the dispersion equations reduce to classical Love equation. The SH-wave velocity has been calculated numerically for both magnetically open circuit and closed circuits. The effect of initial stress and magnetic permeability are illustrated by graphs in both the cases. The velocity of SH-wave decreases with the increment of wave number.

Wave Reflection and Transmission Coefficients of Rubble Mound Breakwaters under Oblique Incident Waves (경사입사파랑중의 사석방파제에 의한 반사율과 투과율에 관한 연구)

  • 배기성;김도삼
    • Journal of Ocean Engineering and Technology
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    • v.15 no.1
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    • pp.31-35
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    • 2001
  • By applying the Boundary Integral Equation Method (BIEM) to obliquely incident for Rubble Mound Breakwater (RMB), wave reflection and transmission the coefficients are studied numerically. The validity of and the present BIEM is confirmed by comparing it with 1)numerical results of the eigenfunction expansion method of Dalrymple et al.(1991), and 2)numerical results of the BIEM of Kojima et al.(1988). Therefore, the characteristics of RMB for obliquely incident waves are investigated according to the variations of the wave period, equivalent linear nondimensional friction coefficient and direction of incident waves. It is revealed that the wave transformations of obliquely incident waves are different from those of normally incident waves.

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The Safety Assessment to Breakwater Systems by Placing Submarine Rectangular Trench (해저 Trench 설치에 의한 방파제 시스템의 안전성 평가)

  • Kim, Sung-Duk
    • Journal of the Korean Society of Safety
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    • v.24 no.1
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    • pp.37-42
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    • 2009
  • The present study is to estimate the effect of wave height affecting at the front face of breakwater systems, when a submarine trench is dredged in the distant offshore from outer breakwater. The wave diffraction field, which is important hydraulic factor in the ocean, is considered to be two dimensional(2D) plane and the configuration of the submarine trench on the sea bed designated by single horizontal long-rectangular system. The numerical simulation is performed by using Green function based on the boundary integral equation and meshed at moving boundary conditions. The results of present numerical simulations are illustrated by applying the normal incidence. It is shown that the ratios of wave height reduction at the front face of breakwater systems are approximately 20% by the effect of placing long trench on the sea bed. This study can effectively be utilized for safety assessment to various breakwater systems in the ocean field.

Estimation of Harbor Responses due to Construction of a New Port in Ulsan Bay

  • Lee, Joong-Woo;Lee, Hoon;Lee, Hak-Sung;Jeon, Min-Su
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2004.08a
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    • pp.217-225
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    • 2004
  • Introduction of wave model, considered the effect of shoaling, refraction, diffraction, partial reflection, bottom friction, breaking at the coastal waters of complex bathymetry, is a very important factor for most coastal engineering design and disaster prevention problems. As waves move from deeper waters to shallow coastal waters, the fundamental wave parameters will change and the wave energy is redistributed along wave crests due to the depth variation, the presence of islands, coastal protection structures, irregularities of the enclosing shore boundaries, and other geological features. Moreover, waves undergo severe change inside the surf zone where wave breaking occurs and in the regions where reflected waves from coastline and structural boundaries interact with the incident waves. Therefore, the application of mild-slope equation model in this field would help for understanding of wave transformation mechanism where many other models could not deal with up to now. The purpose of this study is to form a extended mild-slope equation wave model and make comparison and analysis on variation of harbor responses in the vicinities of Ulsan Harbor and Ulsan New Port, etc. due to construction of New Port in Ulsan Bay. This type of trial might be a milestone for port development in macro scale, where the induced impact analysis in the existing port due to the development could be easily neglected.

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Imaging of Seismic Sources Using Time Reversal Wave Propagation (지진파 역행 전파를 이용한 지진원 영상화)

  • Sheen, Dong-Hoon;Baag, Chang-Eob;Hwang, Eui-Hong;Ryoo, Yong Gyu;Youn, Yong-Hoon
    • 한국지구물리탐사학회:학술대회논문집
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    • 2006.06a
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    • pp.181-186
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    • 2006
  • An imaging method of seismic sources using time-reversal wave propagation is presented. The method is based on the time-reversal invariance and the spatial reciprocity of the wave equation. Time-reversal wave propagation has been used to image anomalous features of a midium in medical imaging, non destructive testing and waveform tomography. Seismogram is the record whose energy is propagated from the seismic source. If time-reversed seismogram propagates back into the medium, seismic energy is concentrated at the origin time of the event and at the source location. In this work, a staggered-grid finite-difference method of the elastic wave equation is parallelized for 3-D wave propagation simulation. With numerical experiments, we show that the time-reversal imaging will enable us to explore the spatio-temporal history of complex earthquake.

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Numerical Experiment on Migration using 45° Wave Equation (45°파동 방정식을 이용한 마이그레이숀 실험)

  • Jang, Hyuk-Jun;Yang, Sung-Jin;Shin, Chang-Soo
    • Economic and Environmental Geology
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    • v.23 no.3
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    • pp.353-358
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    • 1990
  • This paper presents numerical experiments on migration of synthetic seismograms using by $45^{\circ}$ wave equation. The seismograms used are zero-offset seismogram (corresponding to stacked section) on point reflectors, dipping plane reflector, faulted and folded layers. The seismograms are constructed by upward continuation of seismic source wavelets, exploading on subsurface reflection interfaces, to the earth surface. The synthetic seismograms are migrated by downward continuation and imaging. The upward and downward continuations are implemented by solving the $45^{\circ}$ wave equation with the finite-difference method. Migration of the synthetic data used in this study results in relatively accurate reposition of subsurface structures while the synthetic sections are quite different from the structures.

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A step-by-step approach in the time-domain BEM formulation for the scalar wave equation

  • Carrer, J.A.M.;Mansur, W.J.
    • Structural Engineering and Mechanics
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    • v.27 no.6
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    • pp.683-696
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    • 2007
  • This article is concerned with the presentation of a time-domain BEM approach applied to the solution of the scalar wave equation for 2D problems. The basic idea is quite simple: the basic variables of the problem at time $t_n$ (potential and flux) are computed with the results related to the potential and to its time derivative at time $t_{n-1}$ playing the role of "initial conditions". This time-marching scheme needs the computation of the potential and its time derivative at all boundary nodes and internal points, as well as the entire discretization of the domain. The convolution integrals of the standard time-domain BEM formulation, however, are not computed; the matrices assembled, only at the initial time interval, are those related to the potential, flux and to the potential time derivative. Two examples are presented and discussed at the end of the article, in order to verify the accuracy and potentialities of the proposed formulation.

Dispersion Relation including the Effect of Diffusion for E.M. Wave in Solid-State Plasma (고상 프라즈마내에서의 전자파분산측과 확산효과)

  • Cho, Chul
    • 전기의세계
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    • v.20 no.5
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    • pp.15-18
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    • 1971
  • Up to now, there have been numerous investigations about the effect of diffusion on the wave propagation in gaseous plasmas, but not so much in semiconductor magnetoplasmas. However, currently, it becomes the centor of interest to work with the latter problem, and this paper deals with the dispersion equation including diffusion effect in the latter case to see how diffusion affects the equation in which diffusion term is neglected in the first place, and the analysis is based on the assumption that the plasma can be treated as a hydrodynamical fluid, since, from a macroscopic view point, the plasma interacting with a magnetic field can be considered as a magneto-hydrodynamical fluid, an electrically conducting fluid subjected to electromagnetic force, and the system is linear. The results of the relation and computation show that in the non-streaming case the diffusion terms appear in the equation as perturbation terms and the amplitude of the wave vector changes parabolically with the variation of the angular frequency and the longitudinal modes are observed.

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Mach Reflection of Sinusoidally-Modulated Nonlinear Stokes Waves by a Thin Wedge

  • Choi, Hang-S.;Chee, Won-S.
    • Selected Papers of The Society of Naval Architects of Korea
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    • v.1 no.1
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    • pp.45-51
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    • 1993
  • By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

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Evaluation Technique of Concrete Strength Using Impact-Resonance and Combined Method (충격공진법 및 복합법을 이용한 콘크리트의 강도 평가 기법)

  • 이광명;이회근;김동수;김지상
    • Journal of the Korea Concrete Institute
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    • v.11 no.4
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    • pp.157-167
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    • 1999
  • Among several non-destructive testing methods, ultrasonic pulse velocity method and rebound index method have been widely used for the evaluation of concrete strength. However, such methods might not provide accurate estimated results since factors influencing the relationship between strength and either ultrasonic pulse velocity or rebound index are not considered. In this paper, the evaluation method of concrete strength using rod-wave velocity measured by impact-resonance method is proposed. A basic equation is obtained by the linear regression of velocity vs, strength data at specific age and then, aging factor is employed in the equation to consider the difference of the increasing rate between wave velocity and strength. Strengths predicted by the proposed equation agree well with test results. Furthermore, the combined method of rod-wave velocity and rebound index is proposed.